10. d . Solve the differential equation: x2y + 2mg = 1n 2:, y(1) = 2 dx . If y is the solution of the initial value problem 5% = 3(y 1)(y 2) with y(1) = %, what is tlim y(t)? FOO . An integral equation is an equation that contains an unknown function y(m) and an integral that .1!) involves y(m) Solve the given integral equation: y(a:) = 4 + f2t\\/y(t)dt 0 Given a; = 2cos(6) and y = 2sin(0), for 9 E [0, 7r] (a) Eliminate the parameter to nd a Cartesian equation of the curve (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases . Find the length of one arch of the cycloid 93 = 6 sing and y = 1 cosG . Find the area of one loop of the polar curve '1' = 2sin 36 Given r = 2sin(6) for 77/2 5 H S 37r/2. (a) Graph the region described above. (b) Using basic middle school Geometry, nd the area enclosed by the given region. (0) Using integral calculus, nd the area enclosed by the given region. . Eliminate the parameter to nd a Cartesian equation of the curve: 32(75) 2 t, and y(t) 2 315 + 4, t 2 0. Graph the resulting equation Find a formula for the general term an of the sequence: {1,0, 1,0, 1,0, 1,0, ..} 2 12.2 +2 ()0 Determine whether the series converges or diverges by using the integral test: 2 n=1